I appreciate your post Rich and owen and Bruce's responses.

I have a couple of observations:

1) I am always amazed (euphemism for offended) at our use of hyperbole and superlatives in such things. We all know that mathematics and science only has false-summits and that all "ultimates" are perpetual "penultimates", and yet our rhetoric is always laced with absolutes and mega-gigas and supra-ubers.

2) I have long been fascinated at the interplay between language and deep understanding. I studied Esperanto alongside Greek and Latin and Mathematics and Computer Languages in the hopes of finding the right universal tool, or even a toolbox filled with appropriate tools to think/communicate in qualitatively better ways. It was not for naught, and perhaps if I did not have these in my toolbox I would either miss them dearly or not know enough to miss them. But for the most part, my improved thinking/communication feels quantitative, not qualitative.

3) Of the several auxiliary languages, I find Interlingua the easiest to read/understand without any particular training... Esperanto seems to rely heavily on Portuguese vocabulary/roots which are just (un)familiar enough for me to find it difficult. In every case, I am not fluent enough to feel I am able to *think* in these as alternate languages while I do sometimes think in Spanish, in Mathematics, and in several computer languages (for very narrow thinking unfortunately). I wish I could think/percieve in musical structures or holographically, both of which I have a formal understanding of but only limited intuition.

4) I found David Bohm's Rheomode and Dialogue even more compelling because it went deeper than "merely" normalizing somewhat across historical and cultural biases. Esperanto was a great 19th century idea but I felt it did not go nearly far enough. I was (and am still to some extent) enamored of his Holonomics and of course the Rheomode and Dialogue, though the latter two seem under developed and somewhat naive.

- Steve


Thanks, Rich, for the interesting note.

For another kind of completeness, I'll comment that I speak Esperanto.

In the period 1900-1905, approximately, there was a lot of interest
among French intellectuals in the possible use of a constructed
language for the purpose of international communications, with
Esperanto the leading contender. This led to a conference of
scientific groups that actually picked a language, Ido, which was a
modified Esperanto which supposedly "fixed" perceived failings of
Esperanto.

Roughly speaking, Ido rejected the unusual non-European structure of
Esperanto in favor of a more "naturalistic" scheme thought to appeal
more to educated Europeans, and possibly easier for Europeans to read
at sight (but likely to be more difficult to speak or write). The
whole affair was a major schism which damaged the movement to adopt an
easy-to-learn second language.

Both Esperanto and Ido still exist in globally dispersed communities,
but the Esperanto community has by far the largest number of speakers
of all the constructed languages. It is difficult to get good numbers,
but there are probably 50 to 100 thousand fluent speakers. I've even
known a number of native speakers of Esperanto, born to parents who
met in the Esperanto-speaking community and continued to speak the
language at home.

Few educated Americans have ever heard of Esperanto, and what they've
heard is in my experience mostly incorrect. Google Esperanto for vast
amounts of information, much of it accurate.

An interesting math connection: Sometime around 1900 Peano, of
mathematical fame, gave a talk in which he started in pure Latin,
progressively during the talk introduced various simplifications, and
by the end was speaking a much simplified Latin which he proposed for
international use.

Bruce

On Thu, Aug 18, 2011 at 9:41 AM, Owen Densmore<o...@backspaces.net>  wrote:
Wow, thanks Rich.  And the follow-on conversation on the website is also
interesting.
I have to admit the Axiom of Choice has been puzzling to me, why its
importance, how it is applied and so on.
         -- Owen

On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray<rmfor...@gmail.com>  wrote:
  "no one shall expel us from the paradise that Cantor has created",
Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18


http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

Ultimate logic: To infinity and beyond

01 August 2011 by Richard Elwes
Magazine issue 2823.

The mysteries of infinity could lead us to a fantastic structure above
and beyond mathematics as we know it

WHEN David Hilbert left the podium at the Sorbonne in Paris, France,
on 8 August 1900, few of the assembled delegates seemed overly
impressed. According to one contemporary report, the discussion
following his address to the second International Congress of
Mathematicians was "rather desultory". Passions seem to have been more
inflamed by a subsequent debate on whether Esperanto should be adopted
as mathematics' working language.

Yet Hilbert's address set the mathematical agenda for the 20th
century. It crystallised into a list of 23 crucial unanswered
questions, including how to pack spheres to make best use of the
available space, and whether the Riemann hypothesis, which concerns
how the prime numbers are distributed, is true.
<snip>
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